International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 3909-3923
doi:10.1155/IJMMS.2005.3909
Equivalence among some neighborhood structures in fuzzy topology
Cosimo De Mitri
Department of Mathematics “Ennio De Giorgi”, University of Lecce, via Arnesano, C.P. 193, Lecce 73100, Italy
Abstract
We deepen the study of two known neighborhood structures, which here will be called f⋅k-neighborhood structures and f⋅q-neighborhood structures, in the context of Šostak fuzzy topological spaces. In particular, we characterize fuzzy topologies by f⋅k-neighbor-hood structures. Moreover we introduce and discuss the notions of f⋅k-neighborhood prestructure and f⋅m-neighborhood structure in the same context. At last we prove that the three neighborhood structures mentioned above are equivalent.